Capacitance - Lab by bestt571


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									                              ELECTRICAL CAPACITANCE
                                        Physics 230, Lab 3

Objective: To study the capacitance of a parallel plate capacitor, its dependence on the physical
properties of the capacitor, and the laws for combinations of capacitors.

Apparatus: Capacitance meter, wire connectors, a parallel plate capacitor with adjustable plate
separation, plastic slab and two capacitors.

Theory: Any arrangement of two conductors which stores charge is called a capacitor. If
applying a potential difference ΔV across the arrangement produces charges ±Q on the two
conductors, then the capacitance of the arrangement is C =          . The units of C are farad (F),
      1 coulomb
1F =              , or more commonly, the microfarad, 1 µF = 10-6 F, and the picofarad (or micro-
microfarad) 1 pF = 10-12 F. For two parallel plates of area A separated by distance d in a vacuum:
                                                     ε A
                                               C0 = 0 .
The introduction of a dielectric between the plates of an isolated capacitor tends to reduce the
electric field between the plates and hence reduces ΔV with Q staying constant. Therefore, we
expect C to increase with the dielectric in place. If C is the capacitance with a dielectric between
the plates, then κ =      , where κ is called the dielectric constant. Typical values of κ range from
1.0054 for air to 78.6 for water at 25°C.
     When two capacitors are connected in parallel, the total capacitance is the sum of the
individual capacitances:
                                            Ctotal = C1 + C2 .
     When two capacitors are connected in series:
                                              1      1     1
                                                   =    +      .
                                            Ctotal C1 C2

1. Data Acquisition
     Construct an Excel spreadsheet like the attached template. This will be used to record data
from the three experiments below. The shaded areas of the spreadsheet indicate where data will
be recorded.

2. Capacitance of a Parallel Plate Capacitor:
     With the leads removed, and the meter on its most sensitive scale, zero the capacitance
meter. Now connect the two leads to the capacitance meter. These two wires are conductors and
therefore have a capacitance. Set the meter on the most sensitive scale and notice the value of the
capacitance of the wires. Move the wires around to see how the capacitance changes with
separation and configuration. Record the range of capacitance you observe.
     When we connect the wires to the parallel plate capacitor, the resulting arrangement will
really be two capacitors in parallel: the parallel plate capacitor plus the capacitance meter leads.
Since we expect a parallel combination to be the sum of the two capacitances, we must subtract
the capacitance of the wires to obtain the true capacitance of the parallel plate capacitor when we
measure the latter with our meter.
     Use the Vernier caliper to measure the plate separation of the parallel plate capacitor when
the slide scale reads 1.0 cm. The difference between the measured value and 1.0 cm is a
correction factor for the capacitor’s distance scale. It will be necessary to add this distance to the
scale value to obtain the true separation, d. Measure and record the diameter of the plates. Also
record the uncertainty in the measurements of the diameter and the plate separation.
     For a series of 10 measurements, record the capacitance as a function of the plate separation
(as indicated from the sliding scale).
Since the capacitance varies as , if you pick ten equally spaced points, most of your data
points will end up clustered together. You should pick your points so as to evenly space them
            1          1
between         and         .
          1 cm       12 cm

    Note any fluctuations in the meter reading and include them with the uncertainty.

3. Dielectric Constant of a Plastic Slab
     Insert the plastic slab between the plates of the capacitor and gently push the plates flush
against it. Record the plate separation and the capacitance. Carefully remove the slab. If the
plates move, return them to their position before the slab was removed and record the new
     Insert two dielectric slabs against each other and flush with the plates. Again, record the
plate separation and capacitance, remove the slabs and record the new capacitance.

4. Combinations of Capacitors
    For the two small capacitors provided, measure the capacitance of each. Connect the
capacitors in series and then in parallel, recording the capacitance of each combination.

    Calculate the equivalent capacitances for the following arrangements of four capacitors,
each of 8.0 pF capacitance.
1. From your measurements in Part 2 above, plot a graph of capacitance versus the inverse of the
plate separation. Don't forget to subtract the capacitance of the leads and add the zero value of
the plate separation. Use Excel’s Add Trendline function to obtain the equation of the best-fit
straight line through the data and its R2 value. Use Excel’s LINEST array function to find the
standard error of the slope. From the slope of the line and the diameter of the capacitor plates,
use Maple’s Scientific Error Analysis function to compute the permittivity constant, ε 0 and its
standard error.

2. From the measurements of the capacitance with and without the plastic slab, find the dielectric
constant of the slab. Compare the value you obtain for one slab with that of two slabs. What is
the percentage difference?

3. Compute the value of the capacitance of the combinations of the capacitors and compare the
results with what you would expect from the equations given in the Theory section of this
exercise. What might cause the discrepancy?

4. Your lab report should consist of the following:
    (1) the completed spreadsheet and associated graph,
    (2) the error propagation analysis of ε 0 discussed above,
    (3) the answers to the three equivalent capacitance problems above, and
    (4) an abstract describing this experiment.

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